For some work I am doing with matrices with polynomial entries in certain parameters, I need to know for which values of the parameters there is a possibility that the rank of the matrix drops down. I tried using fraction free Gaussian elimination in both linalg and LinearAlgebra. The two methods do not always give the same resulting matrix. Moreover, the matrix is not as simple as it should be. I understand that a Gauss-Bareiss algorithm produces a result which I would be happier with. Does anyone know of such an implementation for Maple? I have been having some difficulty finding an explicit form for the algorithm on the net.
I am converting a complex worksheet from linalg to LinearAlgebra, and
discovered what is to me a serious problem. With linalg, one could use
the basis(A,colspace) command to give a basis of the column space consisting of columns from the original matrix, guaranteed to be in the order in which they appear in the matrix. This is useful in extending a spanning set of a vector space to a basis of a larger space, and allows one to determine exactly which new vectors need to be added. However, the ColumnSpace(A) command in LinearAlgebra does something quite different. It gives a basis of the column space which does not preserve this order, and does not even use the original vectors.